Question

Evaluate: \[\dfrac{7}{12}\]is what percentage of \[\dfrac{5}{6}\]?

Answer 1

Hint:Consider \[\dfrac{7}{12}\] as quantity 1 and \[\dfrac{5}{6}\]as quantity 2. Find what percentage of quantity 1 is quantity 2 by dividing them and multiplying by 100 to get the required percentage.

Complete step-by-step answer:
We know that percentage is a number or ratio that represents a fraction of 100. And we know the percentage is denoted as %. For example 45% is written as forty-five percent, and 45% is equal to \[\dfrac{45}{100}\]or 45 : 100 or 0.45.
Percentages are often used to express a proportionate part of a total. Similarly other examples are 30%, 65%, 80%, 95% etc are percentages which can be expressed in fraction form, ratio or as decimals.
In this question we have been asked to find what percentage of \[\dfrac{7}{12}\]is \[\dfrac{5}{6}\].
Let us take \[\dfrac{7}{12}\]quantity 1 and \[\dfrac{5}{6}\]as quantity 2.
So we need to find what percentage of quantity 1 is quantity 2, which can be written as,
\[=\dfrac{quantity1}{quantity2}\times 100%\]
Now, let us substitute the values of quantity 1 and quantity 2.
\[=\dfrac{\dfrac{7}{12}}{\dfrac{5}{6}}\times 100\]
We know \[\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}\]can be written as \[\left( \dfrac{a\times d}{b\times c} \right)\], which is to multiply the numerator by the reciprocal of the denominator.
Here, a = 7, b = 12, c = 5 and d = 6.
\[\therefore \dfrac{a}{b}\times \dfrac{d}{c}\Rightarrow \dfrac{7}{12}\times \dfrac{6}{5}\times 100\]
Cancel out the like terms and simplify it.
\[\dfrac{7\times 100}{2\times 5}=\dfrac{1\times 100}{10}=7\times 10=70%\]
Hence, \[\dfrac{7}{12}\]is 70% of \[\dfrac{5}{6}\].

Note: If the question was to find what percentage of \[\dfrac{5}{6}\] is \[\dfrac{7}{12}\], then the quantities will get reversed. Here, quantity 1 becomes \[\dfrac{5}{6}\]and quantity 2 becomes \[\dfrac{7}{12}\].
Therefore $\dfrac{Quantity 1}{Quantity 2}\times100%$=$\dfrac{\dfrac{5}{6}}{\dfrac{7}{12}}\times100$
$\Rightarrow\dfrac{5}{6}\times \dfrac{12}{7}\times 100$
$\Rightarrow\dfrac{5\times 2\times 100}{7}=\dfrac{1000}{7}%$
$\Rightarrow142.8\%$